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An approximation result for free discontinuity functionals by means of non‐local energies
Author(s) -
Lussardi Luca
Publication year - 2008
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1019
Subject(s) - discontinuity (linguistics) , mathematics , dimension (graph theory) , sequence (biology) , convergence (economics) , mathematical analysis , pure mathematics , genetics , economics , biology , economic growth
We approximate, in the sense of Γ‐convergence, free discontinuity functionals with linear growth by a sequence of non‐local integral functionals depending on the average of the gradient on small balls. The result extends to a higher dimension what is already proved in ( Ann. Mat. Pura Appl. 2007; 186 (4): 722–744), where there is the proof of the general one‐dimensional case, and in ( ESAIM Control Optim. Calc. Var. 2007; 13 (1):135–162), where the n ‐dimensional case with ϕ=Id is treated. Moreover, we investigate whether it is possible to approximate a given free discontinuity functional by means of non‐local energies. Copyright © 2008 John Wiley & Sons, Ltd.
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